Update (10/7/13): I had to order physical copies of Bill Shields and E.T.A. The Bill Shields CD didn't contain any additional Weather Channel songs, but the E.T.A. CD did! All three were used in station IDs during the holiday season of 1989. They are:
Wow, this has got to be some kind of record! In the last three days, I have been able to solve the mystery of not one, but FOUR songs on my Name That Tune page! On Monday, I received an email from Gary, who gave me the tip about song #1. He mentioned that he had used a program to identify it. Having played the same song for Shazam several times, I was curious what program he was using.
He told me in an email today that it was called Audiggle (no longer available). So I downloaded it, and it was able to identify three more songs! This is awesome because with the exception of the fourth one, I have been trying to identify these songs for many years.
Anyway, here's the list of songs we were able to identify (Thanks Gary!):
061791 is "Sunset Breeze" by Bill Shields, and was a 60 second and 3 minute local forecast song in the final "Prime Time Tonight" playlist.
Unknown16 is "The Apple Bites Back" by Group 87, and was used as a local forecast, Business Travel Forecast, and station ID song!